Econometrics, option 1, the tasks

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Problem 1. On the territory of the region display data for 199X, the
Table 1
Region Number Per capita cost of living in a working-day, rub.
Average daily wages, rubles.
1 81 124
2 77131
3 85 146
4 79139
5 93143
6100159
7 72135
8 90152
9 71127
10 89 154
11 82 127
12111162
Required:
1. A linear regression equation of the pair of.
2. Calculate the linear correlation coefficient and the average error of approximation.
3. To assess the statistical significance of the regression parameters and correlations using the Fischer-test and Student's t-test.
4. Run the forecast wage in the forecast value of per capita subsistence level is 107% of the average.
5. Evaluate the accuracy of prediction by calculating prediction error and the confidence interval.
6. On the same graph to construct the original data and the theoretical line.

Task 2. On the enterprises of the region studied the dependence of production output per worker (thous. Rub.) On the introduction of new fixed assets (the value of the assets at the end of the year) and by the proportion of highly skilled workers in the total number of workers ().
1 6 3.6 9 11 9 6.3 21
2 6 3.6 12 12 11 6.4 22
3 6 3.9 14 13 11 7 24
4 7 4.1 17 14 12 7.5 25
5 7 3.9 18 15 12 7.9 28
July 6 19 4.5 16 13 8.2 30
7 8 5.3 19 17 13 8 30
8 8 5.3 19 18 13 8.6 31
September 9 5.6 20 19 14 9.5 33
October 10 6.8 21 20 14 9 36
Required:
1. Construct a linear multiple regression model. Record the standardized multiple regression equation. On the basis of standardized regression coefficients and average elasticities to rank the factors according to their impact on the result.
2. Find the coefficients of steam, partial and multiple correlation. Analyze them.
3. Find the adjusted coefficient of multiple determination. Compare it with the unadjusted (general) coefficient of determination.
4. With the help of Fisher-test to assess the statistical reliability of the regression equation and the coefficient of determination.
5. Use of private-test to evaluate the appropriateness of including the Fisher equation in the multiple regression and factor after factor after.
6. Write the equation of linear regression of the pair, leaving only one significant factor.

Objective 3
Given the system of econometric equations.
Required
1. Applying a necessary and sufficient condition for identification, determine whether each is identifiable from the equations of the model.
2. Define the method for estimating model parameters.
3. Record in general reduced form model.
Model protectionism Salvator (simplified version):
where - the share of imports in GDP; - The total number of petitions for exemption from customs duties; - The number of satisfied applications for release from customs duties; - A dummy variable equal to 1 for those years in which the dollar in international currency markets was artificially inflated, and 0 - for all other years; - Real GDP; - Net exports; - The current period; - The previous period.

There are conditional data on volumes of electricity consumption (y) inhabitants of the region in 16 quarters.
Required:
1.Postroit autocorrelation function and infer the presence of seasonal variations.
2. Construct the multiplicative model of the time series.
3. Make a forecast for Q2 forward.
t yt t yt
1 5.8 9 7.9
2 4.5 10 5.5
3 5.1 11 6.3
4 9.1 12 10.8
5 7.0 13 9.0
6 5.0 14 6.5
7 6.0 15 7.0
8 10.1 16 11.1

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